Mozilla Data Science Project - 2019

Exploratory Data Analysis (EDA)

This R markdown covers the Exploratory Data Analysis (EDA) on the training dataset of the PRD.

Setting-up

## Loading the needed libraries

library(kableExtra)      # help you build common complex tables and manipulate table styles
library(tidyverse)       # for general data wrangling (includes readr and dplyr)
library(ggplot2)         # to draw statistical plots 
library(plotly)          # to construct interactive 3d plots
library(DataExplorer)    # automated data exploration
library(corrplot)        # to plot nice correlation matrix
library(caret)           # includes several functions to pre-process
library(scales)          # to determining breaks and labels for axes and legends
library(skimr)
library(funModeling) 
library(Hmisc)
library(grid)
library(hrbrthemes)
library(tidyr)
library(viridis)
library(ggpubr)
library(ggthemes)
library(GGally)
library(nortest)

## Loading the training dataset

load("~/GitHub/ff-beta-release-matching/poc/EDA/data_milestone2_df_train_validate_20191025.RData")

Training

## View train dataframe 

kable(head(df_train_f)) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
scroll_box(width = "100%")

client_id	num_active_days	content_crashes	active_hours	uri_count	session_length	search_count	num_bookmarks	num_pages	daily_unique_domains	daily_max_tabs	daily_tabs_opened	startup_ms	daily_num_sessions_started	active_hours_max	uri_count_max	session_length_max	search_count_max	num_pages_max	daily_unique_domains_max	daily_max_tabs_max	daily_tabs_opened_max	startup_ms_max	daily_num_sessions_started_max	label	install_year	profile_age	fxa_configured	sync_configured	is_default_browser	locale	normalized_channel	app_version	default_search_engine	country	timezone_offset	num_addons	cpu_cores	cpu_speed_mhz	cpu_l2_cache_kb	cpu_vendor	memory_mb	os_version	is_wow64	FX_PAGE_LOAD_MS_2_PARENT	TIME_TO_DOM_COMPLETE_MS	TIME_TO_DOM_CONTENT_LOADED_END_MS	TIME_TO_LOAD_EVENT_END_MS	TIME_TO_DOM_INTERACTIVE_MS	TIME_TO_NON_BLANK_PAINT_MS	profile_age_cat	distro_id_norm	timezone_cat	memory_cat	cpu_speed_cat	cpu_cores_cat	is_release	cpu_l2_cache_kb_cat
001cf926-92e3-4587-887e-d3156ba24d82	8	0	1.4215278	76.1250	22.9337499	1.875	11.00	4014.5	6.062500	7.00000	15.00	54176.2500	0.6250000	3.3208333	139	37.007500	6	15464	17.000000	11	29	180095	2	beta	2016	1160	False	False	True	en-US	beta	67	DuckDuckGo	US	-240	8	2	2527	256	Intel	4022	6.1	False	4223.089	5220.036	9079.136	5221.752	6157.840	5198.1300	< 5 years	Mozilla	(-6,-4]	< 4GB	< 3GHz	2	FALSE	< 256
00210163-2123-427e-bb73-398bda9f9eba	5	0	0.8305556	168.2000	2.4390556	0.800	248.75	20599.5	7.866667	3.40000	14.80	3164.0667	1.2000000	1.6708333	325	8.318333	3	20719	17.000000	4	33	4966	2	beta	2016	1079	False	False	False	en-US	beta	67	DuckDuckGo	GB	60	6	2	2394	256	Intel	3810	6.1	False	2148.350	2253.526	1159.979	2146.827	1155.050	1015.9784	< 5 years	Mozilla	(0,2]	< 4GB	< 3GHz	2	FALSE	< 256
0024fd24-4ef5-4771-850a-9e3846597015	2	0	0.5111111	82.0000	0.8712505	2.500	9.00	87.0	2.166667	4.00000	8.00	23977.9444	5.0000000	0.8250000	145	1.464445	5	87	3.333333	6	15	31918	9	beta	2019	745	False	False	True	en-US	beta	67	Google	GB	60	6	4	2394	256	Intel	8124	10.0	False	2699.834	2216.994	1832.642	2119.277	1819.612	1979.7910	< 5 years	Mozilla	(0,2]	< 16GB	< 3GHz	< 4	FALSE	< 256
004f70f7-2576-4de5-94b4-5bf1acdca0a8	8	0	0.3946181	101.8750	4.6785415	7.750	87.00	8882.0	7.750000	9.25000	19.50	1703.3125	1.3750000	1.1625000	210	9.174722	10	9044	13.000000	12	37	3454	2	beta	2018	130	True	True	True	en-US	beta	67	Google	US	-240	10	4	3991	256	Intel	16235	10.0	False	2370.563	2368.195	1614.073	2356.307	1497.652	850.0551	< 6 months	Mozilla	(-6,-4]	< 16GB	< 4GHz	< 4	FALSE	< 256
007c0c11-38e4-476b-a494-d732e15ac159	4	0	0.5930556	167.5000	5.6081245	0.250	13.00	3024.0	1.775000	8.75000	13.75	15285.5375	2.2500000	0.8791667	255	9.059722	1	3552	2.500000	27	36	24592	3	beta	2018	293	False	False	False	en-US	beta	67	Google	US	360	7	2	2659	3072	Intel	3317	10.0	False	4050.417	5106.575	3630.348	5041.016	3618.008	2006.3376	< 2 years	Mozilla	(4,6]	< 4GB	< 3GHz	2	FALSE	> 1024
0294837f-c98f-44ab-8237-30d2eba6c55a	6	0	1.6333333	165.8333	32.4127778	5.500	17.00	7740.7	8.583333	10.33333	20.00	975.2222	0.1666667	3.2319444	323	41.553611	12	7975	13.000000	18	35	1088	1	beta	2019	502	False	False	True	en-US	beta	67	other (non-bundled)	GB	60	7	4	1800	256	Intel	8026	10.0	False	2740.793	2170.362	1482.620	2033.104	1161.901	1034.0580	< 2 years	Mozilla	(0,2]	< 16GB	< 2GHz	< 4	FALSE	< 256

Validation

## View train dataframe 

kable(head(df_validate_f)) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
scroll_box(width = "100%")

client_id	num_active_days	content_crashes	active_hours	uri_count	session_length	search_count	num_bookmarks	num_pages	daily_unique_domains	daily_max_tabs	daily_tabs_opened	startup_ms	daily_num_sessions_started	active_hours_max	uri_count_max	session_length_max	search_count_max	num_pages_max	daily_unique_domains_max	daily_max_tabs_max	daily_tabs_opened_max	startup_ms_max	daily_num_sessions_started_max	label	install_year	profile_age	fxa_configured	sync_configured	is_default_browser	locale	normalized_channel	app_version	default_search_engine	country	timezone_offset	num_addons	cpu_cores	cpu_speed_mhz	cpu_l2_cache_kb	cpu_vendor	memory_mb	os_version	is_wow64	FX_PAGE_LOAD_MS_2_PARENT	TIME_TO_DOM_COMPLETE_MS	TIME_TO_DOM_CONTENT_LOADED_END_MS	TIME_TO_LOAD_EVENT_END_MS	TIME_TO_DOM_INTERACTIVE_MS	TIME_TO_NON_BLANK_PAINT_MS	profile_age_cat	distro_id_norm	timezone_cat	memory_cat	cpu_speed_cat	cpu_cores_cat	is_release	cpu_l2_cache_kb_cat
001cf926-92e3-4587-887e-d3156ba24d82	8	0	1.5369792	71.12500	23.6797916	3.375000	11	1890.571	9.216667	8.500000	16.625	9928.483	0.6250000	2.3250000	120	34.020000	6	2094	20	14	31	17491.667	3	beta	2016	1204	False	False	True	en-US	beta	68	DuckDuckGo	US	-240	7	2	2527	256	Intel	4022	6.1	False	3133.947	3713.308	3748.471	3730.944	2444.799	1972.6632	< 5 years	Mozilla	(-6,-4]	< 4GB	< 3GHz	2	FALSE	< 256
00210163-2123-427e-bb73-398bda9f9eba	2	0	0.1833333	43.50000	0.5619445	1.500000	259	22005.000	5.000000	3.000000	6.000	5413.500	1.0000000	0.2152778	48	0.781111	2	22005	7	4	7	9579.000	1	beta	2016	1124	False	False	False	en-US	beta	68	DuckDuckGo	GB	60	5	2	2394	256	Intel	3810	6.1	False	3226.048	2561.596	1346.836	2523.810	1385.350	935.6222	< 5 years	Mozilla	(0,2]	< 4GB	< 3GHz	2	FALSE	< 256
007c0c11-38e4-476b-a494-d732e15ac159	2	0	0.2423611	89.00000	6.6299995	0.000000	15	7203.000	1.000000	6.500000	9.500	7041.667	1.0000000	0.3222222	99	9.959722	0	7203	1	11	12	9194.333	2	beta	2018	336	False	False	False	en-US	beta	68	Google	US	360	6	2	2659	3072	Intel	3317	10.0	False	4400.155	7244.930	3711.445	7280.457	3929.289	1474.5607	< 2 years	Mozilla	(4,6]	< 4GB	< 3GHz	2	FALSE	> 1024
009ca4e9-874a-4c3e-983d-af0923346efb	3	0	0.1365741	29.66667	0.2358330	0.000000	11	2112.000	1.666667	1.666667	1.000	4644.333	1.6666667	0.1958333	53	0.387222	0	2112	2	2	1	6964.500	2	beta	2013	1606	False	False	True	en-US	beta	68	Google	GB	360	6	2	2594	256	Intel	3965	6.2	False	5909.683	11043.408	5398.452	10410.288	5860.450	4538.1379	< 5 years	Mozilla	(4,6]	< 4GB	< 3GHz	2	FALSE	< 256
0101d568-0c63-4492-9295-ed57ef78207f	3	0	0.3435185	15.66667	24.0802773	0.000000	7	17.000	1.000000	1.666667	1.500	4214.833	0.3333333	0.5083333	19	39.200277	0	18	1	2	2	4215.000	1	beta	2017	6	False	False	False	en-US	beta	68	Google	US	-420	5	4	3093	256	Intel	16274	6.3	True	2306.655	3225.400	2761.783	3493.289	2141.391	2823.6923	< 1 week	Mozilla	(-8,-6]	< 16GB	< 4GHz	< 4	FALSE	< 256
0159675e-15b0-4443-85b1-94de65455636	6	0	0.0946759	18.50000	10.6411113	1.166667	7	115.500	2.666667	3.166667	4.000	2427.250	1.1666667	0.1944444	33	29.938334	2	137	5	6	7	5234.000	2	beta	2019	17	False	False	False	en-US	beta	68	Google	US	-240	5	4	3292	256	Intel	8098	10.0	True	5100.212	6103.080	3665.146	6118.852	3707.192	3391.5286	< 1 month	Mozilla	(-6,-4]	< 16GB	< 4GHz	< 4	FALSE	< 256

Step 1 : Data Inspection

Training

To get introduced to our training dataset, let’s have a look on the basic information of the dataset.

rows	columns	discrete_columns	continuous_columns	all_missing_columns	total_missing_values	complete_rows	total_observations	memory_usage
302819	58	20	38	0	0	302819	17563502	135686992

Validation

To get introduced to our validation dataset, let’s have a look on the basic information of the dataset.

rows	columns	discrete_columns	continuous_columns	all_missing_columns	total_missing_values	complete_rows	total_observations	memory_usage
328042	58	20	38	0	0	328042	19026436	146987912

Observations

• Most of the dataset is composed of continuous variables
• No NAs values (were handled in preprocessing)

Data Structure

Training

Let’s use glimpse function to display a vertical preview of the training dataset. So we can easily preview data type and sample data.

glimpse(df_train_f)

## Observations: 302,819
## Variables: 58
## $ client_id                         <chr> "001cf926-92e3-4587-887e-d31...
## $ num_active_days                   <int> 8, 5, 2, 8, 4, 6, 8, 4, 3, 5...
## $ content_crashes                   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
## $ active_hours                      <dbl> 1.42152778, 0.83055556, 0.51...
## $ uri_count                         <dbl> 76.12500, 168.20000, 82.0000...
## $ session_length                    <dbl> 22.93374988, 2.43905560, 0.8...
## $ search_count                      <dbl> 1.875000, 0.800000, 2.500000...
## $ num_bookmarks                     <dbl> 11.00, 248.75, 9.00, 87.00, ...
## $ num_pages                         <dbl> 4014.5000, 20599.5000, 87.00...
## $ daily_unique_domains              <dbl> 6.062500, 7.866667, 2.166667...
## $ daily_max_tabs                    <dbl> 7.000000, 3.400000, 4.000000...
## $ daily_tabs_opened                 <dbl> 15.000000, 14.800000, 8.0000...
## $ startup_ms                        <dbl> 54176.2500, 3164.0667, 23977...
## $ daily_num_sessions_started        <dbl> 0.6250000, 1.2000000, 5.0000...
## $ active_hours_max                  <dbl> 3.3208333, 1.6708333, 0.8250...
## $ uri_count_max                     <int> 139, 325, 145, 210, 255, 323...
## $ session_length_max                <dbl> 37.007500, 8.318333, 1.46444...
## $ search_count_max                  <int> 6, 3, 5, 10, 1, 12, 29, 0, 0...
## $ num_pages_max                     <dbl> 15464.0, 20719.0, 87.0, 9044...
## $ daily_unique_domains_max          <dbl> 17.000000, 17.000000, 3.3333...
## $ daily_max_tabs_max                <int> 11, 4, 6, 12, 27, 18, 18, 2,...
## $ daily_tabs_opened_max             <int> 29, 33, 15, 37, 36, 35, 170,...
## $ startup_ms_max                    <dbl> 180095.000, 4966.000, 31918....
## $ daily_num_sessions_started_max    <int> 2, 2, 9, 2, 3, 1, 6, 1, 2, 3...
## $ label                             <fct> beta, beta, beta, beta, beta...
## $ install_year                      <dbl> 2016, 2016, 2019, 2018, 2018...
## $ profile_age                       <dbl> 1160, 1079, 745, 130, 293, 5...
## $ fxa_configured                    <fct> False, False, False, True, F...
## $ sync_configured                   <fct> False, False, False, True, F...
## $ is_default_browser                <fct> True, False, True, True, Fal...
## $ locale                            <fct> en-US, en-US, en-US, en-US, ...
## $ normalized_channel                <fct> beta, beta, beta, beta, beta...
## $ app_version                       <dbl> 67, 67, 67, 67, 67, 67, 67, ...
## $ default_search_engine             <fct> DuckDuckGo, DuckDuckGo, Goog...
## $ country                           <fct> US, GB, GB, US, US, GB, GB, ...
## $ timezone_offset                   <int> -240, 60, 60, -240, 360, 60,...
## $ num_addons                        <dbl> 8.00, 6.00, 6.00, 10.00, 7.0...
## $ cpu_cores                         <dbl> 2, 2, 4, 4, 2, 4, 2, 2, 2, 2...
## $ cpu_speed_mhz                     <dbl> 2527, 2394, 2394, 3991, 2659...
## $ cpu_l2_cache_kb                   <dbl> 256, 256, 256, 256, 3072, 25...
## $ cpu_vendor                        <fct> Intel, Intel, Intel, Intel, ...
## $ memory_mb                         <int> 4022, 3810, 8124, 16235, 331...
## $ os_version                        <ord> 6.1, 6.1, 10.0, 10.0, 10.0, ...
## $ is_wow64                          <fct> False, False, False, False, ...
## $ FX_PAGE_LOAD_MS_2_PARENT          <dbl> 4223.0885, 2148.3495, 2699.8...
## $ TIME_TO_DOM_COMPLETE_MS           <dbl> 5220.036, 2253.526, 2216.994...
## $ TIME_TO_DOM_CONTENT_LOADED_END_MS <dbl> 9079.1364, 1159.9791, 1832.6...
## $ TIME_TO_LOAD_EVENT_END_MS         <dbl> 5221.7525, 2146.8265, 2119.2...
## $ TIME_TO_DOM_INTERACTIVE_MS        <dbl> 6157.8399, 1155.0503, 1819.6...
## $ TIME_TO_NON_BLANK_PAINT_MS        <dbl> 5198.1300, 1015.9784, 1979.7...
## $ profile_age_cat                   <ord> < 5 years, < 5 years, < 5 ye...
## $ distro_id_norm                    <fct> Mozilla, Mozilla, Mozilla, M...
## $ timezone_cat                      <fct> "(-6,-4]", "(0,2]", "(0,2]",...
## $ memory_cat                        <ord> < 4GB, < 4GB, < 16GB, < 16GB...
## $ cpu_speed_cat                     <ord> < 3GHz, < 3GHz, < 3GHz, < 4G...
## $ cpu_cores_cat                     <ord> 2, 2, < 4, < 4, 2, < 4, 2, 2...
## $ is_release                        <lgl> FALSE, FALSE, FALSE, FALSE, ...
## $ cpu_l2_cache_kb_cat               <fct> < 256, < 256, < 256, < 256, ...

If we want to get some metrics about data types, zeros, infinite numbers, and missing values, we can use the df_status function.

kable(df_status(df_train_f, FALSE)) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
scroll_box(width = "100%")

variable	q_zeros	p_zeros	q_na	p_na	q_inf	p_inf	type	unique
client_id	0	0.00	0	0	0	0	character	302805
num_active_days	0	0.00	0	0	0	0	integer	8
content_crashes	302819	100.00	0	0	0	0	integer	1
active_hours	7	0.00	0	0	0	0	numeric	180711
uri_count	0	0.00	0	0	0	0	numeric	18610
session_length	0	0.00	0	0	0	0	numeric	289472
search_count	80328	26.53	0	0	0	0	numeric	930
num_bookmarks	472	0.16	0	0	0	0	numeric	19727
num_pages	7	0.00	0	0	0	0	numeric	179391
daily_unique_domains	0	0.00	0	0	0	0	numeric	66058
daily_max_tabs	0	0.00	0	0	0	0	numeric	2888
daily_tabs_opened	0	0.00	0	0	0	0	numeric	4645
startup_ms	0	0.00	0	0	0	0	numeric	276270
daily_num_sessions_started	3100	1.02	0	0	0	0	numeric	654
active_hours_max	7	0.00	0	0	0	0	numeric	39216
uri_count_max	0	0.00	0	0	0	0	integer	3642
session_length_max	0	0.00	0	0	0	0	numeric	188078
search_count_max	80328	26.53	0	0	0	0	integer	140
num_pages_max	7	0.00	0	0	0	0	numeric	76011
daily_unique_domains_max	0	0.00	0	0	0	0	numeric	1996
daily_max_tabs_max	0	0.00	0	0	0	0	integer	541
daily_tabs_opened_max	0	0.00	0	0	0	0	integer	853
startup_ms_max	0	0.00	0	0	0	0	numeric	145192
daily_num_sessions_started_max	3100	1.02	0	0	0	0	integer	85
label	0	0.00	0	0	0	0	factor	2
install_year	0	0.00	0	0	0	0	numeric	21
profile_age	6320	2.09	0	0	0	0	numeric	4127
fxa_configured	0	0.00	0	0	0	0	factor	2
sync_configured	0	0.00	0	0	0	0	factor	2
is_default_browser	0	0.00	0	0	0	0	factor	2
locale	0	0.00	0	0	0	0	factor	2
normalized_channel	0	0.00	0	0	0	0	factor	2
app_version	0	0.00	0	0	0	0	numeric	1
default_search_engine	0	0.00	0	0	0	0	factor	6
country	0	0.00	0	0	0	0	factor	2
timezone_offset	736	0.24	0	0	0	0	integer	35
num_addons	53	0.02	0	0	0	0	numeric	2124
cpu_cores	0	0.00	0	0	0	0	numeric	27
cpu_speed_mhz	0	0.00	0	0	0	0	numeric	1232
cpu_l2_cache_kb	0	0.00	0	0	0	0	numeric	8
cpu_vendor	0	0.00	0	0	0	0	factor	3
memory_mb	0	0.00	0	0	0	0	integer	5893
os_version	0	0.00	0	0	0	0	ordered-factor	5
is_wow64	0	0.00	0	0	0	0	factor	2
FX_PAGE_LOAD_MS_2_PARENT	0	0.00	0	0	0	0	numeric	294778
TIME_TO_DOM_COMPLETE_MS	0	0.00	0	0	0	0	numeric	300964
TIME_TO_DOM_CONTENT_LOADED_END_MS	0	0.00	0	0	0	0	numeric	300503
TIME_TO_LOAD_EVENT_END_MS	0	0.00	0	0	0	0	numeric	301045
TIME_TO_DOM_INTERACTIVE_MS	0	0.00	0	0	0	0	numeric	300036
TIME_TO_NON_BLANK_PAINT_MS	0	0.00	0	0	0	0	numeric	296802
profile_age_cat	0	0.00	0	0	0	0	ordered-factor	6
distro_id_norm	0	0.00	0	0	0	0	factor	4
timezone_cat	0	0.00	0	0	0	0	factor	13
memory_cat	0	0.00	0	0	0	0	ordered-factor	6
cpu_speed_cat	0	0.00	0	0	0	0	ordered-factor	5
cpu_cores_cat	0	0.00	0	0	0	0	ordered-factor	6
is_release	59627	19.69	0	0	0	0	logical	2
cpu_l2_cache_kb_cat	0	0.00	0	0	0	0	factor	4

• q_zeros: quantity of zeros (p_zeros: in percent)
• q_inf: quantity of infinite values (p_inf: in percent)
• q_na: quantity of NA (p_na: in percent)
• type: factor, ordered-factor, numeric, integer or character
• unique: quantity of unique values

Validation

Let’s use glimpse function to display a vertical preview of the validation dataset. So we can easily preview data type and sample data.

glimpse(df_validate_f)

## Observations: 328,042
## Variables: 58
## $ client_id                         <chr> "001cf926-92e3-4587-887e-d31...
## $ num_active_days                   <int> 8, 2, 2, 3, 3, 6, 1, 4, 7, 4...
## $ content_crashes                   <int> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0...
## $ active_hours                      <dbl> 1.53697917, 0.18333333, 0.24...
## $ uri_count                         <dbl> 71.125000, 43.500000, 89.000...
## $ session_length                    <dbl> 23.6797916, 0.5619445, 6.629...
## $ search_count                      <dbl> 3.3750000, 1.5000000, 0.0000...
## $ num_bookmarks                     <dbl> 11.0, 259.0, 15.0, 11.0, 7.0...
## $ num_pages                         <dbl> 1890.5714, 22005.0000, 7203....
## $ daily_unique_domains              <dbl> 9.216667, 5.000000, 1.000000...
## $ daily_max_tabs                    <dbl> 8.500000, 3.000000, 6.500000...
## $ daily_tabs_opened                 <dbl> 16.625, 6.000, 9.500, 1.000,...
## $ startup_ms                        <dbl> 9928.4833, 5413.5000, 7041.6...
## $ daily_num_sessions_started        <dbl> 0.6250000, 1.0000000, 1.0000...
## $ active_hours_max                  <dbl> 2.32500000, 0.21527778, 0.32...
## $ uri_count_max                     <int> 120, 48, 99, 53, 19, 33, 32,...
## $ session_length_max                <dbl> 34.020000, 0.781111, 9.95972...
## $ search_count_max                  <int> 6, 2, 0, 0, 0, 2, 0, 5, 1, 1...
## $ num_pages_max                     <dbl> 2094, 22005, 7203, 2112, 18,...
## $ daily_unique_domains_max          <dbl> 20.000000, 7.000000, 1.00000...
## $ daily_max_tabs_max                <int> 14, 4, 11, 2, 2, 6, 8, 3, 6,...
## $ daily_tabs_opened_max             <int> 31, 7, 12, 1, 2, 7, 13, 71, ...
## $ startup_ms_max                    <dbl> 17491.667, 9579.000, 9194.33...
## $ daily_num_sessions_started_max    <int> 3, 1, 2, 2, 1, 2, 2, 2, 2, 1...
## $ label                             <fct> beta, beta, beta, beta, beta...
## $ install_year                      <dbl> 2016, 2016, 2018, 2013, 2017...
## $ profile_age                       <dbl> 1204, 1124, 336, 1606, 6, 17...
## $ fxa_configured                    <fct> False, False, False, False, ...
## $ sync_configured                   <fct> False, False, False, False, ...
## $ is_default_browser                <fct> True, False, False, True, Fa...
## $ locale                            <fct> en-US, en-US, en-US, en-US, ...
## $ normalized_channel                <fct> beta, beta, beta, beta, beta...
## $ app_version                       <dbl> 68, 68, 68, 68, 68, 68, 68, ...
## $ default_search_engine             <fct> DuckDuckGo, DuckDuckGo, Goog...
## $ country                           <fct> US, GB, US, GB, US, US, US, ...
## $ timezone_offset                   <int> -240, 60, 360, 360, -420, -2...
## $ num_addons                        <dbl> 7.0, 5.0, 6.0, 6.0, 5.0, 5.0...
## $ cpu_cores                         <dbl> 2, 2, 2, 2, 4, 4, 1, 2, 4, 3...
## $ cpu_speed_mhz                     <dbl> 2527, 2394, 2659, 2594, 3093...
## $ cpu_l2_cache_kb                   <dbl> 256, 256, 3072, 256, 256, 25...
## $ cpu_vendor                        <fct> Intel, Intel, Intel, Intel, ...
## $ memory_mb                         <int> 4022, 3810, 3317, 3965, 1627...
## $ os_version                        <ord> 6.1, 6.1, 10.0, 6.2, 6.3, 10...
## $ is_wow64                          <fct> False, False, False, False, ...
## $ FX_PAGE_LOAD_MS_2_PARENT          <dbl> 3133.947, 3226.048, 4400.155...
## $ TIME_TO_DOM_COMPLETE_MS           <dbl> 3713.308, 2561.596, 7244.930...
## $ TIME_TO_DOM_CONTENT_LOADED_END_MS <dbl> 3748.4715, 1346.8361, 3711.4...
## $ TIME_TO_LOAD_EVENT_END_MS         <dbl> 3730.944, 2523.810, 7280.457...
## $ TIME_TO_DOM_INTERACTIVE_MS        <dbl> 2444.7985, 1385.3500, 3929.2...
## $ TIME_TO_NON_BLANK_PAINT_MS        <dbl> 1972.6632, 935.6222, 1474.56...
## $ profile_age_cat                   <ord> < 5 years, < 5 years, < 2 ye...
## $ distro_id_norm                    <fct> Mozilla, Mozilla, Mozilla, M...
## $ timezone_cat                      <fct> "(-6,-4]", "(0,2]", "(4,6]",...
## $ memory_cat                        <ord> < 4GB, < 4GB, < 4GB, < 4GB, ...
## $ cpu_speed_cat                     <ord> < 3GHz, < 3GHz, < 3GHz, < 3G...
## $ cpu_cores_cat                     <ord> 2, 2, 2, 2, < 4, < 4, 1, 2, ...
## $ is_release                        <lgl> FALSE, FALSE, FALSE, FALSE, ...
## $ cpu_l2_cache_kb_cat               <fct> < 256, < 256, > 1024, < 256,...

If we want to get some metrics about data types, zeros, infinite numbers, and missing values, we can use the df_status function.

kable(df_status(df_train_f, FALSE)) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
scroll_box(width = "100%")

variable	q_zeros	p_zeros	q_na	p_na	q_inf	p_inf	type	unique
client_id	0	0.00	0	0	0	0	character	302805
num_active_days	0	0.00	0	0	0	0	integer	8
content_crashes	302819	100.00	0	0	0	0	integer	1
active_hours	7	0.00	0	0	0	0	numeric	180711
uri_count	0	0.00	0	0	0	0	numeric	18610
session_length	0	0.00	0	0	0	0	numeric	289472
search_count	80328	26.53	0	0	0	0	numeric	930
num_bookmarks	472	0.16	0	0	0	0	numeric	19727
num_pages	7	0.00	0	0	0	0	numeric	179391
daily_unique_domains	0	0.00	0	0	0	0	numeric	66058
daily_max_tabs	0	0.00	0	0	0	0	numeric	2888
daily_tabs_opened	0	0.00	0	0	0	0	numeric	4645
startup_ms	0	0.00	0	0	0	0	numeric	276270
daily_num_sessions_started	3100	1.02	0	0	0	0	numeric	654
active_hours_max	7	0.00	0	0	0	0	numeric	39216
uri_count_max	0	0.00	0	0	0	0	integer	3642
session_length_max	0	0.00	0	0	0	0	numeric	188078
search_count_max	80328	26.53	0	0	0	0	integer	140
num_pages_max	7	0.00	0	0	0	0	numeric	76011
daily_unique_domains_max	0	0.00	0	0	0	0	numeric	1996
daily_max_tabs_max	0	0.00	0	0	0	0	integer	541
daily_tabs_opened_max	0	0.00	0	0	0	0	integer	853
startup_ms_max	0	0.00	0	0	0	0	numeric	145192
daily_num_sessions_started_max	3100	1.02	0	0	0	0	integer	85
label	0	0.00	0	0	0	0	factor	2
install_year	0	0.00	0	0	0	0	numeric	21
profile_age	6320	2.09	0	0	0	0	numeric	4127
fxa_configured	0	0.00	0	0	0	0	factor	2
sync_configured	0	0.00	0	0	0	0	factor	2
is_default_browser	0	0.00	0	0	0	0	factor	2
locale	0	0.00	0	0	0	0	factor	2
normalized_channel	0	0.00	0	0	0	0	factor	2
app_version	0	0.00	0	0	0	0	numeric	1
default_search_engine	0	0.00	0	0	0	0	factor	6
country	0	0.00	0	0	0	0	factor	2
timezone_offset	736	0.24	0	0	0	0	integer	35
num_addons	53	0.02	0	0	0	0	numeric	2124
cpu_cores	0	0.00	0	0	0	0	numeric	27
cpu_speed_mhz	0	0.00	0	0	0	0	numeric	1232
cpu_l2_cache_kb	0	0.00	0	0	0	0	numeric	8
cpu_vendor	0	0.00	0	0	0	0	factor	3
memory_mb	0	0.00	0	0	0	0	integer	5893
os_version	0	0.00	0	0	0	0	ordered-factor	5
is_wow64	0	0.00	0	0	0	0	factor	2
FX_PAGE_LOAD_MS_2_PARENT	0	0.00	0	0	0	0	numeric	294778
TIME_TO_DOM_COMPLETE_MS	0	0.00	0	0	0	0	numeric	300964
TIME_TO_DOM_CONTENT_LOADED_END_MS	0	0.00	0	0	0	0	numeric	300503
TIME_TO_LOAD_EVENT_END_MS	0	0.00	0	0	0	0	numeric	301045
TIME_TO_DOM_INTERACTIVE_MS	0	0.00	0	0	0	0	numeric	300036
TIME_TO_NON_BLANK_PAINT_MS	0	0.00	0	0	0	0	numeric	296802
profile_age_cat	0	0.00	0	0	0	0	ordered-factor	6
distro_id_norm	0	0.00	0	0	0	0	factor	4
timezone_cat	0	0.00	0	0	0	0	factor	13
memory_cat	0	0.00	0	0	0	0	ordered-factor	6
cpu_speed_cat	0	0.00	0	0	0	0	ordered-factor	5
cpu_cores_cat	0	0.00	0	0	0	0	ordered-factor	6
is_release	59627	19.69	0	0	0	0	logical	2
cpu_l2_cache_kb_cat	0	0.00	0	0	0	0	factor	4

• q_zeros: quantity of zeros (p_zeros: in percent)
• q_inf: quantity of infinite values (p_inf: in percent)
• q_na: quantity of NA (p_na: in percent)
• type: factor, ordered-factor, numeric, integer or character
• unique: quantity of unique values

Observations

Are all the variables in the correct data type?

None. It seems that this has already been dealt with in preprocessing.

Any variables with lots of zeros?

Yes. Variables with lots of zeros may not be useful for modeling and, in some cases, they may dramatically bias the model. For example, the content_crashes is 100% equal to zero.

Any variables with lots of NAs?

None. Good news.

Any high cardinality variable?

Factor/categorical variables with a high number of different values (~30) tend to do overfitting if the categories have low cardinality.

Step 2 : Beta vs Release

Training

df_release <- df_train_f[which(df_train_f$label == 'release'), ]
df_beta <- df_train_f[which(df_train_f$label == 'beta'), ]

f <- freq(df_train_f$label)

summary(df_release)

##   client_id         num_active_days content_crashes  active_hours   
##  Length:243192      Min.   :1.00    Min.   :0       Min.   :0.0000  
##  Class :character   1st Qu.:4.00    1st Qu.:0       1st Qu.:0.2686  
##  Mode  :character   Median :6.00    Median :0       Median :0.5744  
##                     Mean   :5.57    Mean   :0       Mean   :0.8469  
##                     3rd Qu.:8.00    3rd Qu.:0       3rd Qu.:1.1266  
##                     Max.   :8.00    Max.   :0       Max.   :7.1222  
##                                                                     
##    uri_count       session_length      search_count    num_bookmarks     
##  Min.   :   1.00   Min.   : 0.01926   Min.   : 0.000   Min.   :    0.00  
##  1st Qu.:  44.33   1st Qu.: 2.15904   1st Qu.: 0.000   1st Qu.:   10.00  
##  Median :  96.67   Median : 6.33512   Median : 0.875   Median :   26.00  
##  Mean   : 156.24   Mean   : 9.28218   Mean   : 2.377   Mean   :  158.94  
##  3rd Qu.: 197.00   3rd Qu.:13.66085   3rd Qu.: 3.000   3rd Qu.:   85.21  
##  Max.   :2391.25   Max.   :91.06639   Max.   :45.750   Max.   :18632.00  
##                                                                          
##    num_pages      daily_unique_domains daily_max_tabs    daily_tabs_opened
##  Min.   :     0   Min.   : 1.000       Min.   :  0.625   Min.   :  1.000  
##  1st Qu.:  1022   1st Qu.: 2.283       1st Qu.:  2.500   1st Qu.:  4.000  
##  Median :  5536   Median : 3.600       Median :  3.714   Median :  8.833  
##  Mean   : 17331   Mean   : 4.968       Mean   :  6.200   Mean   : 17.093  
##  3rd Qu.: 19681   3rd Qu.: 6.071       3rd Qu.:  6.000   3rd Qu.: 19.167  
##  Max.   :168416   Max.   :39.375       Max.   :445.375   Max.   :347.500  
##                                                                           
##    startup_ms      daily_num_sessions_started active_hours_max 
##  Min.   :    261   Min.   : 0.000             Min.   : 0.0000  
##  1st Qu.:   1433   1st Qu.: 1.250             1st Qu.: 0.5403  
##  Median :   3231   Median : 2.000             Median : 1.1542  
##  Mean   :   9832   Mean   : 2.889             Mean   : 1.6251  
##  3rd Qu.:   8395   3rd Qu.: 3.500             3rd Qu.: 2.1903  
##  Max.   :5358123   Max.   :32.250             Max.   :23.9667  
##                                                                
##  uri_count_max     session_length_max search_count_max  num_pages_max   
##  Min.   :    1.0   Min.   :  0.0306   Min.   :  0.000   Min.   :     0  
##  1st Qu.:   86.0   1st Qu.:  4.4085   1st Qu.:  0.000   1st Qu.:  1142  
##  Median :  196.0   Median : 11.7017   Median :  2.000   Median :  5706  
##  Mean   :  321.4   Mean   : 18.2107   Mean   :  5.434   Mean   : 17519  
##  3rd Qu.:  400.0   3rd Qu.: 26.1284   3rd Qu.:  7.000   3rd Qu.: 19922  
##  Max.   :18032.0   Max.   :384.2883   Max.   :217.000   Max.   :172543  
##                                                                         
##  daily_unique_domains_max daily_max_tabs_max daily_tabs_opened_max
##  Min.   :  1.000          Min.   :   1.000   Min.   :   1.00      
##  1st Qu.:  3.125          1st Qu.:   4.000   1st Qu.:   7.00      
##  Median :  6.000          Median :   6.000   Median :  17.00      
##  Mean   :  8.552          Mean   :   9.318   Mean   :  33.27      
##  3rd Qu.: 11.000          3rd Qu.:   9.000   3rd Qu.:  38.00      
##  Max.   :100.000          Max.   :2425.000   Max.   :2410.00      
##                                                                   
##  startup_ms_max     daily_num_sessions_started_max     label       
##  Min.   :     271   Min.   :  0.000                beta   :     0  
##  1st Qu.:    2310   1st Qu.:  2.000                release:243192  
##  Median :    5695   Median :  4.000                                
##  Mean   :   25484   Mean   :  5.249                                
##  3rd Qu.:   16705   3rd Qu.:  6.000                                
##  Max.   :39562826   Max.   :100.000                                
##                                                                    
##   install_year   profile_age     fxa_configured sync_configured
##  Min.   :2000   Min.   :   0.0   False:197466   False:194974   
##  1st Qu.:2016   1st Qu.: 257.0   True : 45726   True : 48218   
##  Median :2018   Median : 698.0                                 
##  Mean   :2017   Mean   : 894.7                                 
##  3rd Qu.:2018   3rd Qu.:1374.0                                 
##  Max.   :2019   Max.   :6922.0                                 
##                                                                
##  is_default_browser   locale       normalized_channel  app_version
##  False:101700       en-GB: 23966   beta   :     0     Min.   :67  
##  True :141492       en-US:219226   release:243192     1st Qu.:67  
##                                                       Median :67  
##                                                       Mean   :67  
##                                                       3rd Qu.:67  
##                                                       Max.   :67  
##                                                                   
##          default_search_engine country     timezone_offset 
##  Bing               :  4442    GB: 36767   Min.   :-720.0  
##  DuckDuckGo         :  8328    US:206425   1st Qu.:-300.0  
##  Google             :203781                Median :-240.0  
##  other (bundled)    :   737                Mean   :-238.7  
##  other (non-bundled): 25549                3rd Qu.:-240.0  
##  Yahoo              :   355                Max.   : 720.0  
##                                                            
##    num_addons       cpu_cores      cpu_speed_mhz   cpu_l2_cache_kb
##  Min.   : 0.000   Min.   : 1.000   Min.   :  792   Min.   : 128   
##  1st Qu.: 4.000   1st Qu.: 2.000   1st Qu.: 2261   1st Qu.: 256   
##  Median : 5.000   Median : 2.000   Median : 2712   Median : 256   
##  Mean   : 5.652   Mean   : 3.143   Mean   : 2711   Mean   : 626   
##  3rd Qu.: 6.000   3rd Qu.: 4.000   3rd Qu.: 3193   3rd Qu.: 512   
##  Max.   :61.000   Max.   :40.000   Max.   :15077   Max.   :6144   
##                                                                   
##  cpu_vendor       memory_mb      os_version      is_wow64     
##  AMD  : 36898   Min.   :   512   Other:    15   False:230560  
##  Intel:206286   1st Qu.:  4011   6.1  : 65588   True : 12632  
##  Other:     8   Median :  8069   6.2  :  1756                 
##                 Mean   :  9444   6.3  : 13121                 
##                 3rd Qu.: 12144   10.0 :162712                 
##                 Max.   :524254                                
##                                                               
##  FX_PAGE_LOAD_MS_2_PARENT TIME_TO_DOM_COMPLETE_MS
##  Min.   :    3.814        Min.   :   15          
##  1st Qu.: 1900.609        1st Qu.: 1728          
##  Median : 2657.412        Median : 2498          
##  Mean   : 3030.073        Mean   : 3291          
##  3rd Qu.: 3797.899        3rd Qu.: 3878          
##  Max.   :10000.000        Max.   :50000          
##                                                  
##  TIME_TO_DOM_CONTENT_LOADED_END_MS TIME_TO_LOAD_EVENT_END_MS
##  Min.   :   15.62                  Min.   :   15            
##  1st Qu.: 1120.26                  1st Qu.: 1614            
##  Median : 1629.36                  Median : 2300            
##  Mean   : 2290.86                  Mean   : 3017            
##  3rd Qu.: 2592.47                  3rd Qu.: 3534            
##  Max.   :44262.02                  Max.   :50000            
##                                                             
##  TIME_TO_DOM_INTERACTIVE_MS TIME_TO_NON_BLANK_PAINT_MS   profile_age_cat 
##  Min.   :   22.89           Min.   :    27.0           < 1 week  : 7613  
##  1st Qu.:  978.79           1st Qu.:   777.2           < 1 month : 6802  
##  Median : 1374.34           Median :  1095.7           < 6 months:32979  
##  Mean   : 1796.62           Mean   :  1445.7           < 2 years :77214  
##  3rd Qu.: 2079.06           3rd Qu.:  1651.2           < 5 years :86054  
##  Max.   :34688.55           Max.   :100000.0           > 5 years :32530  
##                                                                          
##  distro_id_norm      timezone_cat     memory_cat     cpu_speed_cat   
##  acer   :  2619   (-6,-4]  :146732   < 1GB :   346   < 1GHz :   452  
##  Mozilla:237022   (-8,-6]  : 54613   < 2GB :  5534   < 2GHz : 38361  
##  other  :  2351   (0,2]    : 35955   < 4GB : 66120   < 3GHz :123428  
##  Yahoo  :  1200   (4,6]    :  2165   < 6GB : 15982   < 4GHz : 76780  
##                   [-12,-10]:   958   < 16GB:144433   > 16GHz:  4171  
##                   (6,8]    :   870   > 16GB: 10777                   
##                   (Other)  :  1899                                   
##  cpu_cores_cat is_release     cpu_l2_cache_kb_cat
##  1   :  3122   Mode:logical   < 1024: 22370      
##  2   :120526   TRUE:243192    < 256 :179679      
##  < 4 :104846                  < 512 : 13262      
##  < 8 : 13778                  > 1024: 27881      
##  < 16:   745                                     
##  > 16:   175                                     
## 

summary(df_beta)

##   client_id         num_active_days content_crashes  active_hours   
##  Length:59627       Min.   :1.000   Min.   :0       Min.   :0.0000  
##  Class :character   1st Qu.:4.000   1st Qu.:0       1st Qu.:0.2250  
##  Mode  :character   Median :6.000   Median :0       Median :0.5310  
##                     Mean   :5.346   Mean   :0       Mean   :0.8237  
##                     3rd Qu.:8.000   3rd Qu.:0       3rd Qu.:1.1029  
##                     Max.   :8.000   Max.   :0       Max.   :7.2901  
##                                                                     
##    uri_count       session_length       search_count     num_bookmarks    
##  Min.   :   1.00   Min.   :  0.01667   Min.   : 0.0000   Min.   :    0.0  
##  1st Qu.:  37.00   1st Qu.:  2.52840   1st Qu.: 0.0000   1st Qu.:   10.0  
##  Median :  86.67   Median :  7.71056   Median : 0.8333   Median :   26.0  
##  Mean   : 152.75   Mean   : 12.29620   Mean   : 2.4506   Mean   :  242.5  
##  3rd Qu.: 188.50   3rd Qu.: 19.57926   3rd Qu.: 2.8333   3rd Qu.:   96.0  
##  Max.   :2931.00   Max.   :240.80486   Max.   :51.0000   Max.   :40401.0  
##                                                                           
##    num_pages      daily_unique_domains daily_max_tabs    
##  Min.   :     1   Min.   : 1.000       Min.   :   1.000  
##  1st Qu.:   686   1st Qu.: 2.167       1st Qu.:   2.600  
##  Median :  4186   Median : 3.562       Median :   4.250  
##  Mean   : 17363   Mean   : 5.060       Mean   :   9.604  
##  3rd Qu.: 18605   3rd Qu.: 6.167       3rd Qu.:   8.000  
##  Max.   :179658   Max.   :44.000       Max.   :1012.625  
##                                                          
##  daily_tabs_opened   startup_ms       daily_num_sessions_started
##  Min.   :  1.00    Min.   :     269   Min.   : 0.000            
##  1st Qu.:  4.00    1st Qu.:    2102   1st Qu.: 1.000            
##  Median :  9.00    Median :    5088   Median : 1.667            
##  Mean   : 20.49    Mean   :   25836   Mean   : 2.369            
##  3rd Qu.: 21.75    3rd Qu.:   12619   3rd Qu.: 2.875            
##  Max.   :518.25    Max.   :17109506   Max.   :32.833            
##                                                                 
##  active_hours_max uri_count_max   session_length_max  search_count_max 
##  Min.   : 0.000   Min.   :    1   Min.   :   0.0214   Min.   :  0.000  
##  1st Qu.: 0.450   1st Qu.:   68   1st Qu.:   4.8778   1st Qu.:  0.000  
##  Median : 1.064   Median :  172   Median :  14.8089   Median :  2.000  
##  Mean   : 1.578   Mean   :  311   Mean   :  22.7066   Mean   :  5.636  
##  3rd Qu.: 2.165   3rd Qu.:  382   3rd Qu.:  31.5190   3rd Qu.:  7.000  
##  Max.   :24.983   Max.   :15626   Max.   :1255.3822   Max.   :188.000  
##                                                                        
##  num_pages_max    daily_unique_domains_max daily_max_tabs_max
##  Min.   :     1   Min.   :  1.000          Min.   :   1.00   
##  1st Qu.:   785   1st Qu.:  3.000          1st Qu.:   4.00   
##  Median :  4340   Median :  5.500          Median :   6.00   
##  Mean   : 17559   Mean   :  8.744          Mean   :  13.81   
##  3rd Qu.: 18886   3rd Qu.: 11.000          3rd Qu.:  12.00   
##  Max.   :180456   Max.   :100.000          Max.   :3149.00   
##                                                              
##  daily_tabs_opened_max startup_ms_max      daily_num_sessions_started_max
##  Min.   :   1.00       Min.   :      269   Min.   : 0.000                
##  1st Qu.:   6.00       1st Qu.:     3186   1st Qu.: 2.000                
##  Median :  17.00       Median :     8389   Median : 3.000                
##  Mean   :  39.65       Mean   :    86290   Mean   : 4.281                
##  3rd Qu.:  42.00       3rd Qu.:    23149   3rd Qu.: 5.000                
##  Max.   :3302.00       Max.   :106338296   Max.   :88.000                
##                                                                          
##      label        install_year   profile_age     fxa_configured
##  beta   :59627   Min.   :1993   Min.   :   0.0   False:51826   
##  release:    0   1st Qu.:2017   1st Qu.: 271.0   True : 7801   
##                  Median :2018   Median : 711.0                 
##                  Mean   :2017   Mean   : 893.8                 
##                  3rd Qu.:2018   3rd Qu.:1354.0                 
##                  Max.   :2019   Max.   :7051.0                 
##                                                                
##  sync_configured is_default_browser   locale      normalized_channel
##  False:51267     False:26001        en-GB: 2581   beta   :59627     
##  True : 8360     True :33626        en-US:57046   release:    0     
##                                                                     
##                                                                     
##                                                                     
##                                                                     
##                                                                     
##   app_version         default_search_engine country    timezone_offset 
##  Min.   :67   Bing               :  833     GB:17333   Min.   :-720.0  
##  1st Qu.:67   DuckDuckGo         : 2630     US:42294   1st Qu.:-300.0  
##  Median :67   Google             :52211                Median :-240.0  
##  Mean   :67   other (bundled)    :  125                Mean   :-143.9  
##  3rd Qu.:67   other (non-bundled): 3828                3rd Qu.:  60.0  
##  Max.   :67   Yahoo              :    0                Max.   : 840.0  
##                                                                        
##    num_addons        cpu_cores      cpu_speed_mhz   cpu_l2_cache_kb 
##  Min.   :  0.000   Min.   : 1.000   Min.   :  798   Min.   : 128.0  
##  1st Qu.:  6.000   1st Qu.: 2.000   1st Qu.: 2200   1st Qu.: 256.0  
##  Median :  7.000   Median : 2.000   Median : 2594   Median : 256.0  
##  Mean   :  7.855   Mean   : 2.976   Mean   : 2678   Mean   : 679.9  
##  3rd Qu.:  8.000   3rd Qu.: 4.000   3rd Qu.: 3192   3rd Qu.: 512.0  
##  Max.   :170.000   Max.   :36.000   Max.   :37214   Max.   :6144.0  
##                                                                     
##  cpu_vendor      memory_mb      os_version     is_wow64    
##  AMD  : 8757   Min.   :   511   Other:   16   False:44733  
##  Intel:50820   1st Qu.:  3984   6.1  :17123   True :14894  
##  Other:   50   Median :  8031   6.2  :  674                
##                Mean   :  8965   6.3  : 3785                
##                3rd Qu.: 10238   10.0 :38029                
##                Max.   :262078                              
##                                                            
##  FX_PAGE_LOAD_MS_2_PARENT TIME_TO_DOM_COMPLETE_MS
##  Min.   :    1            Min.   :    7          
##  1st Qu.: 2028            1st Qu.: 1894          
##  Median : 2952            Median : 2918          
##  Mean   : 3464            Mean   : 4389          
##  3rd Qu.: 4487            3rd Qu.: 5106          
##  Max.   :10000            Max.   :50000          
##                                                  
##  TIME_TO_DOM_CONTENT_LOADED_END_MS TIME_TO_LOAD_EVENT_END_MS
##  Min.   :   18.17                  Min.   :    7            
##  1st Qu.: 1217.61                  1st Qu.: 1796            
##  Median : 1856.04                  Median : 2739            
##  Mean   : 2737.64                  Mean   : 4127            
##  3rd Qu.: 3185.18                  3rd Qu.: 4758            
##  Max.   :50000.00                  Max.   :50000            
##                                                             
##  TIME_TO_DOM_INTERACTIVE_MS TIME_TO_NON_BLANK_PAINT_MS   profile_age_cat 
##  Min.   :   40.84           Min.   :    7.0            < 1 week  : 1590  
##  1st Qu.: 1081.05           1st Qu.:  845.6            < 1 month : 2485  
##  Median : 1618.02           Median : 1251.7            < 6 months: 8173  
##  Mean   : 2404.39           Mean   : 1833.7            < 2 years :18155  
##  3rd Qu.: 2738.66           3rd Qu.: 2052.5            < 5 years :21807  
##  Max.   :50000.00           Max.   :90081.0            > 5 years : 7417  
##                                                                          
##  distro_id_norm   timezone_cat    memory_cat    cpu_speed_cat  
##  acer   :    3   (-6,-4]:26166   < 1GB :  378   < 1GHz :  157  
##  Mozilla:59615   (0,2]  :15927   < 2GB : 2924   < 2GHz : 9968  
##  other  :    7   (-8,-6]:10863   < 4GB :18788   < 3GHz :30935  
##  Yahoo  :    2   (4,6]  : 3244   < 6GB : 3558   < 4GHz :17258  
##                  (6,8]  : 1410   < 16GB:31147   > 16GHz: 1309  
##                  (2,4]  : 1119   > 16GB: 2832                  
##                  (Other):  898                                 
##  cpu_cores_cat is_release      cpu_l2_cache_kb_cat
##  1   : 1224    Mode :logical   < 1024: 6014       
##  2   :32916    FALSE:59627     < 256 :42540       
##  < 4 :22776                    < 512 : 3321       
##  < 8 : 2507                    > 1024: 7752       
##  < 16:  180                                       
##  > 16:   24                                       
## 

Validation

df_v_release <- df_validate_f[which(df_validate_f$label == 'release'), ]
df_v_beta <- df_validate_f[which(df_validate_f$label == 'beta'), ]

f <- freq(df_validate_f$label)

summary(df_v_release)

##   client_id         num_active_days content_crashes  active_hours   
##  Length:257697      Min.   :1.00    Min.   :0       Min.   :0.0000  
##  Class :character   1st Qu.:4.00    1st Qu.:0       1st Qu.:0.2641  
##  Mode  :character   Median :6.00    Median :0       Median :0.5752  
##                     Mean   :5.71    Mean   :0       Mean   :0.8525  
##                     3rd Qu.:8.00    3rd Qu.:0       3rd Qu.:1.1399  
##                     Max.   :8.00    Max.   :0       Max.   :7.2205  
##                                                                     
##    uri_count       session_length      search_count    num_bookmarks     
##  Min.   :   1.00   Min.   : 0.01572   Min.   : 0.000   Min.   :    0.00  
##  1st Qu.:  44.00   1st Qu.: 2.31995   1st Qu.: 0.000   1st Qu.:   10.00  
##  Median :  97.43   Median : 6.78083   Median : 1.000   Median :   25.33  
##  Mean   : 158.72   Mean   : 9.70679   Mean   : 2.446   Mean   :  158.03  
##  3rd Qu.: 200.14   3rd Qu.:14.77410   3rd Qu.: 3.000   3rd Qu.:   84.00  
##  Max.   :2483.17   Max.   :90.44222   Max.   :45.000   Max.   :20002.14  
##                                                                          
##    num_pages        daily_unique_domains daily_max_tabs    
##  Min.   :     0.0   Min.   : 1.000       Min.   :  0.5714  
##  1st Qu.:   991.3   1st Qu.: 2.287       1st Qu.:  2.5000  
##  Median :  5308.0   Median : 3.651       Median :  3.8000  
##  Mean   : 17089.9   Mean   : 5.112       Mean   :  6.3472  
##  3rd Qu.: 19359.8   3rd Qu.: 6.250       3rd Qu.:  6.2857  
##  Max.   :168812.1   Max.   :42.400       Max.   :449.3333  
##                                                            
##  daily_tabs_opened   startup_ms       daily_num_sessions_started
##  Min.   :  1.000   Min.   :     239   Min.   : 0.000            
##  1st Qu.:  4.000   1st Qu.:    1567   1st Qu.: 1.167            
##  Median :  8.857   Median :    3346   Median : 2.000            
##  Mean   : 17.187   Mean   :   27279   Mean   : 2.831            
##  3rd Qu.: 19.500   3rd Qu.:    7770   3rd Qu.: 3.375            
##  Max.   :357.000   Max.   :22594812   Max.   :32.250            
##                                                                 
##  active_hours_max  uri_count_max     session_length_max search_count_max 
##  Min.   : 0.0000   Min.   :    1.0   Min.   :  0.0197   Min.   :  0.000  
##  1st Qu.: 0.5375   1st Qu.:   86.0   1st Qu.:  4.7883   1st Qu.:  0.000  
##  Median : 1.1653   Median :  199.0   Median : 12.8028   Median :  3.000  
##  Mean   : 1.6370   Mean   :  328.4   Mean   : 18.6141   Mean   :  5.634  
##  3rd Qu.: 2.2208   3rd Qu.:  409.0   3rd Qu.: 27.0975   3rd Qu.:  7.000  
##  Max.   :25.4403   Max.   :18524.0   Max.   :524.5456   Max.   :208.000  
##                                                                          
##  num_pages_max    daily_unique_domains_max daily_max_tabs_max
##  Min.   :     0   Min.   :  1.000          Min.   :   1.00   
##  1st Qu.:  1113   1st Qu.:  3.200          1st Qu.:   4.00   
##  Median :  5490   Median :  6.000          Median :   6.00   
##  Mean   : 17289   Mean   :  8.837          Mean   :   9.54   
##  3rd Qu.: 19606   3rd Qu.: 11.000          3rd Qu.:  10.00   
##  Max.   :170532   Max.   :100.000          Max.   :2215.00   
##                                                              
##  daily_tabs_opened_max startup_ms_max      daily_num_sessions_started_max
##  Min.   :   1.00       Min.   :      239   Min.   :  0.00                
##  1st Qu.:   7.00       1st Qu.:     2618   1st Qu.:  2.00                
##  Median :  17.00       Median :     5997   Median :  4.00                
##  Mean   :  33.54       Mean   :    95160   Mean   :  5.18                
##  3rd Qu.:  38.00       3rd Qu.:    14981   3rd Qu.:  6.00                
##  Max.   :2342.00       Max.   :171712978   Max.   :184.00                
##                                                                          
##      label         install_year   profile_age     fxa_configured
##  beta   :     0   Min.   :2000   Min.   :   0.0   False:207292  
##  release:257697   1st Qu.:2017   1st Qu.: 235.0   True : 50405  
##                   Median :2018   Median : 673.0                 
##                   Mean   :2017   Mean   : 883.9                 
##                   3rd Qu.:2019   3rd Qu.:1368.0                 
##                   Max.   :2019   Max.   :6972.0                 
##                                                                 
##  sync_configured is_default_browser   locale       normalized_channel
##  False:205539    False:108253       en-GB: 24771   beta   :     0    
##  True : 52158    True :149444       en-US:232926   release:257697    
##                                                                      
##                                                                      
##                                                                      
##                                                                      
##                                                                      
##   app_version         default_search_engine country     timezone_offset 
##  Min.   :68   Bing               :  5142    GB: 37712   Min.   :-720.0  
##  1st Qu.:68   DuckDuckGo         :  9598    US:219985   1st Qu.:-300.0  
##  Median :68   Google             :225161                Median :-240.0  
##  Mean   :68   missing            :    33                Mean   :-240.5  
##  3rd Qu.:68   other (bundled)    :   682                3rd Qu.:-240.0  
##  Max.   :68   other (non-bundled): 16655                Max.   : 780.0  
##               Yahoo              :   426                                
##    num_addons       cpu_cores      cpu_speed_mhz   cpu_l2_cache_kb 
##  Min.   : 0.000   Min.   : 1.000   Min.   :  768   Min.   : 128.0  
##  1st Qu.: 4.000   1st Qu.: 2.000   1st Qu.: 2261   1st Qu.: 256.0  
##  Median : 5.000   Median : 3.000   Median : 2712   Median : 256.0  
##  Mean   : 5.678   Mean   : 3.192   Mean   : 2713   Mean   : 610.8  
##  3rd Qu.: 6.000   3rd Qu.: 4.000   3rd Qu.: 3193   3rd Qu.: 512.0  
##  Max.   :71.000   Max.   :50.000   Max.   :28900   Max.   :6144.0  
##                                                                    
##  cpu_vendor       memory_mb       os_version      is_wow64     
##  AMD  : 38180   Min.   :    512   Other:    16   False:244710  
##  Intel:219506   1st Qu.:   4021   6.1  : 65859   True : 12987  
##  Other:    11   Median :   8073   6.2  :  1819                 
##                 Mean   :   9720   6.3  : 13387                 
##                 3rd Qu.:  12180   10.0 :176616                 
##                 Max.   :1572801                                
##                                                                
##  FX_PAGE_LOAD_MS_2_PARENT TIME_TO_DOM_COMPLETE_MS
##  Min.   :    1            Min.   :   28.78       
##  1st Qu.: 1815            1st Qu.: 1627.44       
##  Median : 2520            Median : 2328.42       
##  Mean   : 2894            Mean   : 3039.55       
##  3rd Qu.: 3590            3rd Qu.: 3547.01       
##  Max.   :10000            Max.   :47816.25       
##                                                  
##  TIME_TO_DOM_CONTENT_LOADED_END_MS TIME_TO_LOAD_EVENT_END_MS
##  Min.   :   23.71                  Min.   :   28.95         
##  1st Qu.: 1105.90                  1st Qu.: 1542.78         
##  Median : 1592.19                  Median : 2182.18         
##  Mean   : 2146.62                  Mean   : 2837.31         
##  3rd Qu.: 2481.38                  3rd Qu.: 3301.45         
##  Max.   :48375.15                  Max.   :47816.25         
##                                                             
##  TIME_TO_DOM_INTERACTIVE_MS TIME_TO_NON_BLANK_PAINT_MS   profile_age_cat 
##  Min.   :   19.86           Min.   :    16.71          < 1 week  : 8309  
##  1st Qu.:  973.66           1st Qu.:   775.88          < 1 month : 9838  
##  Median : 1362.24           Median :  1093.90          < 6 months:35158  
##  Mean   : 1761.98           Mean   :  1448.36          < 2 years :81811  
##  3rd Qu.: 2037.65           3rd Qu.:  1652.08          < 5 years :87688  
##  Max.   :41404.35           Max.   :100000.00          > 5 years :34893  
##                                                                          
##  distro_id_norm      timezone_cat     memory_cat     cpu_speed_cat   
##  acer   :  2790   (-6,-4]  :157717   < 1GB :   316   < 1GHz :   448  
##  Mozilla:251379   (-8,-6]  : 57182   < 2GB :  5300   < 2GHz : 40596  
##  other  :  2313   (0,2]    : 36782   < 4GB : 66569   < 3GHz :130993  
##  Yahoo  :  1215   (4,6]    :  2209   < 6GB : 16419   < 4GHz : 81353  
##                   [-12,-10]:   957   < 16GB:156709   > 16GHz:  4307  
##                   (6,8]    :   797   > 16GB: 12384                   
##                   (Other)  :  2053                                   
##  cpu_cores_cat is_release     cpu_l2_cache_kb_cat
##  1   :  3101   Mode:logical   < 1024: 22578      
##  2   :124514   TRUE:257697    < 256 :192910      
##  < 4 :112698                  < 512 : 13930      
##  < 8 : 16276                  > 1024: 28279      
##  < 16:   900                                     
##  > 16:   208                                     
## 

summary(df_v_beta)

##   client_id         num_active_days content_crashes  active_hours   
##  Length:70345       Min.   :1.000   Min.   :0       Min.   :0.0000  
##  Class :character   1st Qu.:3.000   1st Qu.:0       1st Qu.:0.2074  
##  Mode  :character   Median :5.000   Median :0       Median :0.5028  
##                     Mean   :4.913   Mean   :0       Mean   :0.7988  
##                     3rd Qu.:7.000   3rd Qu.:0       3rd Qu.:1.0601  
##                     Max.   :8.000   Max.   :0       Max.   :7.5403  
##                                                                     
##    uri_count       session_length     search_count    num_bookmarks    
##  Min.   :   1.00   Min.   :  0.020   Min.   : 0.000   Min.   :    0.0  
##  1st Qu.:  33.25   1st Qu.:  2.213   1st Qu.: 0.000   1st Qu.:    9.0  
##  Median :  80.50   Median :  7.154   Median : 0.750   Median :   23.0  
##  Mean   : 146.33   Mean   : 12.337   Mean   : 2.324   Mean   :  225.4  
##  3rd Qu.: 179.00   3rd Qu.: 18.739   3rd Qu.: 2.667   3rd Qu.:   85.0  
##  Max.   :2983.00   Max.   :286.698   Max.   :50.000   Max.   :39519.0  
##                                                                        
##    num_pages        daily_unique_domains daily_max_tabs   
##  Min.   :     0.0   Min.   : 1.000       Min.   :  0.400  
##  1st Qu.:   543.3   1st Qu.: 2.125       1st Qu.:  2.500  
##  Median :  3347.5   Median : 3.500       Median :  4.125  
##  Mean   : 15614.0   Mean   : 5.148       Mean   :  9.020  
##  3rd Qu.: 15660.6   3rd Qu.: 6.167       3rd Qu.:  7.750  
##  Max.   :177583.0   Max.   :49.292       Max.   :910.400  
##                                                           
##  daily_tabs_opened   startup_ms       daily_num_sessions_started
##  Min.   :  1.00    Min.   :     289   Min.   : 0.000            
##  1st Qu.:  3.50    1st Qu.:    2219   1st Qu.: 1.000            
##  Median :  8.50    Median :    5016   Median : 1.667            
##  Mean   : 20.03    Mean   :   50073   Mean   : 2.398            
##  3rd Qu.: 21.00    3rd Qu.:   11210   3rd Qu.: 3.000            
##  Max.   :554.00    Max.   :50660200   Max.   :32.000            
##                                                                 
##  active_hours_max  uri_count_max     session_length_max search_count_max
##  Min.   : 0.0000   Min.   :    1.0   Min.   :  0.0411   Min.   :  0.0   
##  1st Qu.: 0.3917   1st Qu.:   57.0   1st Qu.:  4.0028   1st Qu.:  0.0   
##  Median : 0.9625   Median :  152.0   Median : 12.9614   Median :  2.0   
##  Mean   : 1.4712   Mean   :  287.3   Mean   : 22.2730   Mean   :  5.1   
##  3rd Qu.: 2.0014   3rd Qu.:  352.0   3rd Qu.: 28.9514   3rd Qu.:  6.0   
##  Max.   :31.1278   Max.   :17548.0   Max.   :922.2850   Max.   :313.0   
##                                                                         
##  num_pages_max    daily_unique_domains_max daily_max_tabs_max
##  Min.   :     0   Min.   :  1.000          Min.   :   1.00   
##  1st Qu.:   620   1st Qu.:  3.000          1st Qu.:   4.00   
##  Median :  3513   Median :  5.200          Median :   6.00   
##  Mean   : 15780   Mean   :  8.582          Mean   :  12.83   
##  3rd Qu.: 15872   3rd Qu.: 10.500          3rd Qu.:  11.00   
##  Max.   :182555   Max.   :100.000          Max.   :1779.00   
##                                                              
##  daily_tabs_opened_max startup_ms_max      daily_num_sessions_started_max
##  Min.   :   1.0        Min.   :      289   Min.   :  0.000               
##  1st Qu.:   5.0        1st Qu.:     3296   1st Qu.:  1.000               
##  Median :  15.0        Median :     7801   Median :  3.000               
##  Mean   :  37.3        Mean   :   142010   Mean   :  4.141               
##  3rd Qu.:  39.0        3rd Qu.:    18500   3rd Qu.:  5.000               
##  Max.   :2551.0        Max.   :251665490   Max.   :110.000               
##                                                                          
##      label        install_year   profile_age     fxa_configured
##  beta   :70345   Min.   :2000   Min.   :   0.0   False:59564   
##  release:    0   1st Qu.:2017   1st Qu.: 213.0   True :10781   
##                  Median :2018   Median : 690.0                 
##                  Mean   :2017   Mean   : 875.3                 
##                  3rd Qu.:2019   3rd Qu.:1329.0                 
##                  Max.   :2019   Max.   :7095.0                 
##                                                                
##  sync_configured is_default_browser   locale      normalized_channel
##  False:58484     False:32258        en-GB: 2997   beta   :70345     
##  True :11861     True :38087        en-US:67348   release:    0     
##                                                                     
##                                                                     
##                                                                     
##                                                                     
##                                                                     
##   app_version         default_search_engine country    timezone_offset 
##  Min.   :68   Bing               : 1011     GB:20569   Min.   :-720.0  
##  1st Qu.:68   DuckDuckGo         : 2936     US:49776   1st Qu.:-300.0  
##  Median :68   Google             :62032                Median :-240.0  
##  Mean   :68   missing            :   35                Mean   :-129.9  
##  3rd Qu.:68   other (bundled)    :   63                3rd Qu.:  60.0  
##  Max.   :68   other (non-bundled): 4266                Max.   : 840.0  
##               Yahoo              :    2                                
##    num_addons       cpu_cores      cpu_speed_mhz   cpu_l2_cache_kb 
##  Min.   : 0.000   Min.   : 1.000   Min.   :  633   Min.   : 128.0  
##  1st Qu.: 5.000   1st Qu.: 2.000   1st Qu.: 2195   1st Qu.: 256.0  
##  Median : 6.000   Median : 2.000   Median : 2594   Median : 256.0  
##  Mean   : 6.883   Mean   : 2.954   Mean   : 2656   Mean   : 674.6  
##  3rd Qu.: 7.000   3rd Qu.: 4.000   3rd Qu.: 3192   3rd Qu.: 512.0  
##  Max.   :76.000   Max.   :32.000   Max.   :37221   Max.   :6144.0  
##                                                                    
##  cpu_vendor      memory_mb      os_version     is_wow64    
##  AMD  :10123   Min.   :   511   Other:   12   False:50246  
##  Intel:60149   1st Qu.:  3981   6.1  :20330   True :20099  
##  Other:   73   Median :  7973   6.2  :  781                
##                Mean   :  8796   6.3  : 4768                
##                3rd Qu.:  8189   10.0 :44454                
##                Max.   :294902                              
##                                                            
##  FX_PAGE_LOAD_MS_2_PARENT TIME_TO_DOM_COMPLETE_MS
##  Min.   :    1            Min.   :   34          
##  1st Qu.: 2044            1st Qu.: 1902          
##  Median : 3045            Median : 3024          
##  Mean   : 3593            Mean   : 4597          
##  3rd Qu.: 4727            3rd Qu.: 5481          
##  Max.   :10000            Max.   :50000          
##                                                  
##  TIME_TO_DOM_CONTENT_LOADED_END_MS TIME_TO_LOAD_EVENT_END_MS
##  Min.   :   30.71                  Min.   :   34            
##  1st Qu.: 1271.67                  1st Qu.: 1816            
##  Median : 2001.34                  Median : 2857            
##  Mean   : 2896.94                  Mean   : 4376            
##  3rd Qu.: 3454.47                  3rd Qu.: 5204            
##  Max.   :41450.65                  Max.   :50000            
##                                                             
##  TIME_TO_DOM_INTERACTIVE_MS TIME_TO_NON_BLANK_PAINT_MS   profile_age_cat 
##  Min.   :   26              Min.   :     4.0           < 1 week  : 1869  
##  1st Qu.: 1143              1st Qu.:   889.2           < 1 month : 3232  
##  Median : 1764              Median :  1358.9           < 6 months:10897  
##  Mean   : 2627              Mean   :  2014.8           < 2 years :20628  
##  3rd Qu.: 3069              3rd Qu.:  2286.5           < 5 years :25035  
##  Max.   :49619              Max.   :100000.0           > 5 years : 8684  
##                                                                          
##  distro_id_norm   timezone_cat    memory_cat    cpu_speed_cat  
##  acer   :    4   (-6,-4]:29163   < 1GB :  396   < 1GHz :  217  
##  Mozilla:70331   (0,2]  :18167   < 2GB : 4078   < 2GHz :12505  
##  other  :    7   (-8,-6]:13002   < 4GB :22890   < 3GHz :36310  
##  Yahoo  :    3   (4,6]  : 4667   < 6GB : 4105   < 4GHz :19935  
##                  (6,8]  : 2289   < 16GB:35628   > 16GHz: 1378  
##                  (2,4]  : 1932   > 16GB: 3248                  
##                  (Other): 1125                                 
##  cpu_cores_cat is_release      cpu_l2_cache_kb_cat
##  1   : 1399    Mode :logical   < 1024: 7181       
##  2   :39571    FALSE:70345     < 256 :50220       
##  < 4 :26174                    < 512 : 3911       
##  < 8 : 2970                    > 1024: 9033       
##  < 16:  209                                       
##  > 16:   22                                       
## 

Step 3 - Analyzing Discrete Variables

Training

## Frequency distribution release dataframe
plot_bar(df_release, ggtheme = theme_minimal(base_size = 15))

## Frequency distribution beta dataframe
plot_bar(df_beta, ggtheme = theme_minimal(base_size = 15))

Validation

## Frequency distribution release dataframe
plot_bar(df_v_release, ggtheme = theme_minimal(base_size = 15))

## Frequency distribution beta dataframe
plot_bar(df_v_beta, ggtheme = theme_minimal(base_size = 15))

Step 4 - Analyzing Continuos Variables

Training

## View histogram of release dataset
plot_histogram(df_release, ggtheme = theme_minimal(base_size = 15))

## View histogram of beta dataset
plot_histogram(df_beta, ggtheme = theme_minimal(base_size = 15))

Validation

## View histogram of release dataset
plot_histogram(df_release, ggtheme = theme_minimal(base_size = 15))

## View histogram of beta dataset
plot_histogram(df_beta, ggtheme = theme_minimal(base_size = 15))

Observations

• My first impression is that user engagement metrics might be a good path to follow

Ploting Density Curves

## Training
t <- ggplot(data=df_train_f, aes(x=uri_count, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) + xlim(0, 1000) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="URI Count", y = "Density") +
    theme_ipsum()

## Validation
v <- ggplot(data=df_validate_f, aes(x=uri_count, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) + xlim(0, 1000) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="URI Count", y = "Density") +
    theme_ipsum()

plot_grid(t, v, ncol=2, labels = c("Train", "Validate")) ## Set up a 2 x 2 plotting space

## Training
t <- ggplot(data=df_train_f, aes(x=active_hours, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="Active Hours", y = "Density") +
    theme_ipsum()

## Validation
v <- ggplot(data=df_validate_f, aes(x=active_hours, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="Active Hours", y = "Density") +
    theme_ipsum()

plot_grid(t, v, ncol=2, labels = c("Train", "Validate")) ## Set up a 2 x 2 plotting space

## Training
t <- ggplot(data=df_train_f, aes(x=num_pages, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) + xlim(0, 50000) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="Num Pages", y = "Density") +
    theme_ipsum()

## Validation
v <- ggplot(data=df_validate_f, aes(x=num_pages, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) + xlim(0, 50000) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="Num Pages", y = "Density") +
    theme_ipsum()

plot_grid(t, v, ncol=2, labels = c("Train", "Validate")) ## Set up a 2 x 2 plotting space

## Training
t <- ggplot(data=df_train_f, aes(x=session_length, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) + xlim(0, 75) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="Session Length", y = "Density") +
    theme_ipsum()

## Validation
v <- ggplot(data=df_validate_f, aes(x=session_length, group=label, fill=label)) +
    geom_density(adjust=1.5, alpha=0.6) + xlim(0, 75) +
    scale_fill_viridis(discrete=TRUE) +
    scale_color_viridis(discrete=TRUE) +
    labs(x="Session Length", y = "Density") +
    theme_ipsum()

plot_grid(t, v, ncol=2, labels = c("Train", "Validate")) ## Set up a 2 x 2 plotting space

User Engagement Continuous Metrics

This section will focus only on user engagement continuous metrics. So, we are going to analyze the following metrics:

• num_active_days
• active_hours
• active_hours_max
• uri_count
• uri_count_max
• session_length
• session_length_max
• search_count
• search_count_max
• num_bookmarks
• num_pages
• num_pages_max
• num_addons
• daily_unique_domains
• daily_unique_domains_max
• daily_max_tabs
• daily_max_tabs_max
• daily_tabs_opened
• daily_tabs_opened_max
• daily_num_sessions_started
• daily_num_sessions_started_max
• startup_ms
• install_year
• profile_age
• timezone_offset
• memory_mb
• cpu_cores
• cpu_speed_mhz
• cpu_l2_cache_kb

Training

kable(text_tbl) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
scroll_box(width = "100%")

	beta_num_active_days	release_num_active_days	beta_active_hours	release_active_hours	beta_active_hours_max	release_active_hours_max	beta_uri_count	release_uri_count	beta_uri_count_max	release_uri_count_max	beta_session_length	release_session_length	beta_session_length_max	release_session_length_max	beta_search_count	release_search_count	beta_search_count_max	release_search_count_max	beta_num_bookmarks	release_num_bookmarks	beta_num_pages	release_num_pages	beta_num_pages_max	release_num_pages_max	beta_daily_unique_domains	release_daily_unique_domains	beta_daily_max_tabs	release_daily_max_tabs	beta_daily_tabs_opened	release_daily_tabs_opened	beta_daily_num_sessions_started	release_daily_num_sessions_started	beta_daily_unique_domains_max	release_daily_unique_domains_max	beta_daily_max_tabs_max	release_daily_max_tabs_max	beta_daily_tabs_opened_max	release_daily_tabs_opened_max	beta_daily_num_sessions_started_max	release_daily_num_sessions_started_max	beta_startup_ms	release_startup_ms	beta_install_year	release_install_year	beta_profile_age	release_profile_age	beta_timezone_offset	release_timezone_offset	beta_memory_mb	release_memory_mb	beta_cpu_cores	release_cpu_cores	beta_cpu_speed_mhz	release_cpu_speed_mhz	beta_cpu_l2_cache_kb	release_cpu_l2_cache_kb
Min.	1.000000	1.000000	0.0000000	0.0000000	0.000000	0.0000000	1.00000	1.00000	1.0000	1.0000	0.0166665	0.0192595	0.021389	0.030556	0.0000000	0.000000	0.000000	0.000000	0.0000	0.0000	1.000	0.000	1.00	0.00	1.000000	1.000000	1.000000	0.625000	1.00000	1.000000	0.000000	0.000000	1.00000	1.000000	1.00000	1.000000	1.00000	1.00000	0.000000	0.000000	269.000	261.128	1993.000	2000.000	0.0000	0.0000	-720.000	-720.000	511.000	512.000	1.000000	1.000000	798.000	792.00	128.0000	128.0000
1st Qu.	4.000000	4.000000	0.2250000	0.2686111	0.450000	0.5402778	37.00000	44.33333	68.0000	86.0000	2.5284028	2.1590431	4.877777	4.408542	0.0000000	0.000000	0.000000	0.000000	10.0000	10.0000	686.000	1022.125	785.00	1142.00	2.166667	2.283333	2.600000	2.500000	4.00000	4.000000	1.000000	1.250000	3.00000	3.125000	4.00000	4.000000	6.00000	7.00000	2.000000	2.000000	2102.206	1432.677	2017.000	2016.000	271.0000	257.0000	-300.000	-300.000	3984.000	4011.000	2.000000	2.000000	2200.000	2261.00	256.0000	256.0000
Median	6.000000	6.000000	0.5309524	0.5744444	1.063889	1.1541667	86.66667	96.66667	172.0000	196.0000	7.7105554	6.3351191	14.808889	11.701666	0.8333333	0.875000	2.000000	2.000000	26.0000	26.0000	4185.667	5536.000	4340.00	5705.50	3.562500	3.600000	4.250000	3.714286	9.00000	8.833333	1.666667	2.000000	5.50000	6.000000	6.00000	6.000000	17.00000	17.00000	3.000000	4.000000	5088.010	3231.339	2018.000	2018.000	711.0000	698.0000	-240.000	-240.000	8031.000	8069.000	2.000000	2.000000	2594.000	2712.00	256.0000	256.0000
Mean	5.346169	5.569842	0.8236611	0.8468557	1.577508	1.6251135	152.74550	156.24224	311.0213	321.3891	12.2961990	9.2821806	22.706568	18.210749	2.4506498	2.376504	5.636171	5.434352	242.4878	158.9390	17363.463	17330.600	17558.93	17518.75	5.060464	4.968328	9.603628	6.200080	20.49191	17.092979	2.368895	2.888602	8.74361	8.552061	13.81149	9.317556	39.64786	33.27059	4.281399	5.248573	25835.963	9832.051	2017.138	2017.064	893.7534	894.7365	-143.855	-238.714	8965.156	9443.657	2.975699	3.143089	2678.209	2710.62	679.9325	625.9611
3rd Qu.	8.000000	8.000000	1.1028646	1.1265956	2.165278	2.1902778	188.50000	197.00000	382.0000	400.0000	19.5792560	13.6608531	31.519026	26.128403	2.8333333	3.000000	7.000000	7.000000	96.0000	85.2125	18605.464	19680.625	18885.50	19922.00	6.166667	6.070833	8.000000	6.000000	21.75000	19.166667	2.875000	3.500000	11.00000	11.000000	12.00000	9.000000	42.00000	38.00000	5.000000	6.000000	12618.764	8394.891	2018.000	2018.000	1354.0000	1374.0000	60.000	-240.000	10238.000	12144.000	4.000000	4.000000	3192.000	3193.00	512.0000	512.0000
Max.	8.000000	8.000000	7.2901042	7.1222222	24.983333	23.9666667	2931.00000	2391.25000	15626.0000	18032.0000	240.8048605	91.0663890	1255.382223	384.288333	51.0000000	45.750000	188.000000	217.000000	40401.0000	18632.0000	179657.500	168416.286	180456.00	172543.00	44.000000	39.375000	1012.625000	445.375000	518.25000	347.500000	32.833333	32.250000	100.00000	100.000000	3149.00000	2425.000000	3302.00000	2410.00000	88.000000	100.000000	17109505.514	5358122.833	2019.000	2019.000	7051.0000	6922.0000	840.000	720.000	262078.000	524254.000	36.000000	40.000000	37214.000	15077.00	6144.0000	6144.0000

Validation

kable(text_tbl_v) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
scroll_box(width = "100%")

	beta_num_active_days	release_num_active_days	beta_active_hours	release_active_hours	beta_active_hours_max	release_active_hours_max	beta_uri_count	release_uri_count	beta_uri_count_max	release_uri_count_max	beta_session_length	release_session_length	beta_session_length_max	release_session_length_max	beta_search_count	release_search_count	beta_search_count_max	release_search_count_max	beta_num_bookmarks	release_num_bookmarks	beta_num_pages	release_num_pages	beta_num_pages_max	release_num_pages_max	beta_daily_unique_domains	release_daily_unique_domains	beta_daily_max_tabs	release_daily_max_tabs	beta_daily_tabs_opened	release_daily_tabs_opened	beta_daily_num_sessions_started	release_daily_num_sessions_started	beta_daily_unique_domains_max	release_daily_unique_domains_max	beta_daily_max_tabs_max	release_daily_max_tabs_max	beta_daily_tabs_opened_max	release_daily_tabs_opened_max	beta_daily_num_sessions_started_max	release_daily_num_sessions_started_max	beta_startup_ms	release_startup_ms	beta_install_year	release_install_year	beta_profile_age	release_profile_age	beta_timezone_offset	release_timezone_offset	beta_memory_mb	release_memory_mb	beta_cpu_cores	release_cpu_cores	beta_cpu_speed_mhz	release_cpu_speed_mhz	beta_cpu_l2_cache_kb	release_cpu_l2_cache_kb
Min.	1.000000	1.000000	0.0000000	0.0000000	0.0000000	0.000000	1.0000	1.00000	1.0000	1.0000	0.0199998	0.0157222	0.041111	0.019722	0.000000	0.000000	0.000000	0.000000	0.0000	0.00000	0.0000	0.0000	0.00	0.00	1.000000	1.000000	0.400000	0.5714286	1.00000	1.000000	0.000000	0.000000	1.00000	1.000000	1.00000	1.000000	1.00000	1.00000	0.000000	0.000000	289.000	2.388333e+02	2000.000	2000.000	0.0000	0.000	-720.0000	-720.0000	511.000	512.000	1.000000	1.000000	633.00	768.000	128.0000	128.0000
1st Qu.	3.000000	4.000000	0.2074074	0.2640873	0.3916667	0.537500	33.2500	44.00000	57.0000	86.0000	2.2133335	2.3199533	4.002778	4.788333	0.000000	0.000000	0.000000	0.000000	9.0000	10.00000	543.3333	991.3333	620.00	1113.00	2.125000	2.287037	2.500000	2.5000000	3.50000	4.000000	1.000000	1.166667	3.00000	3.200000	4.00000	4.000000	5.00000	7.00000	1.000000	2.000000	2218.863	1.567167e+03	2017.000	2017.000	213.0000	235.000	-300.0000	-300.0000	3981.000	4021.000	2.000000	2.000000	2195.00	2261.000	256.0000	256.0000
Median	5.000000	6.000000	0.5027778	0.5751736	0.9625000	1.165278	80.5000	97.42857	152.0000	199.0000	7.1543749	6.7808331	12.961389	12.802778	0.750000	1.000000	2.000000	3.000000	23.0000	25.33333	3347.5000	5308.0000	3513.00	5490.00	3.500000	3.651190	4.125000	3.8000000	8.50000	8.857143	1.666667	2.000000	5.20000	6.000000	6.00000	6.000000	15.00000	17.00000	3.000000	4.000000	5015.522	3.345629e+03	2018.000	2018.000	690.0000	673.000	-240.0000	-240.0000	7973.000	8073.000	2.000000	3.000000	2594.00	2712.000	256.0000	256.0000
Mean	4.912574	5.710307	0.7988445	0.8524956	1.4711888	1.636961	146.3339	158.71931	287.3003	328.3892	12.3367205	9.7067904	22.272966	18.614122	2.324319	2.446479	5.100206	5.633558	225.4153	158.03362	15614.0379	17089.9304	15779.79	17289.08	5.148112	5.112258	9.019717	6.3471824	20.03166	17.187064	2.398131	2.831202	8.58199	8.837358	12.82845	9.539785	37.29553	33.54423	4.141417	5.180103	50072.589	2.727928e+04	2017.255	2017.194	875.2575	883.857	-129.9082	-240.4712	8795.994	9719.802	2.954155	3.191904	2656.31	2712.603	674.5779	610.7777
3rd Qu.	7.000000	8.000000	1.0600694	1.1399306	2.0013889	2.220833	179.0000	200.14286	352.0000	409.0000	18.7390970	14.7740975	28.951388	27.097500	2.666667	3.000000	6.000000	7.000000	85.0000	84.00000	15660.6250	19359.8333	15872.00	19606.00	6.166667	6.250000	7.750000	6.2857143	21.00000	19.500000	3.000000	3.375000	10.50000	11.000000	11.00000	10.000000	39.00000	38.00000	5.000000	6.000000	11210.000	7.770437e+03	2019.000	2019.000	1329.0000	1368.000	60.0000	-240.0000	8189.000	12180.000	4.000000	4.000000	3192.00	3193.000	512.0000	512.0000
Max.	8.000000	8.000000	7.5402778	7.2204861	31.1277778	25.440278	2983.0000	2483.16667	17548.0000	18524.0000	286.6983330	90.4422220	922.285000	524.545556	50.000000	45.000000	313.000000	208.000000	39519.0000	20002.14286	177583.0000	168812.1429	182555.00	170532.00	49.291667	42.400000	910.400000	449.3333333	554.00000	357.000000	32.000000	32.250000	100.00000	100.000000	1779.00000	2215.000000	2551.00000	2342.00000	110.000000	184.000000	50660199.500	2.259481e+07	2019.000	2019.000	7095.0000	6972.000	840.0000	780.0000	294902.000	1572801.000	32.000000	50.000000	37221.00	28900.000	6144.0000	6144.0000

Comparing Two Continuous Distributions

Training

The QQ plot can be used to compare two continuous distributions.

par(mfrow = c(2, 2))  ## Set up a 2 x 2 plotting space

## QQ plot in R to compare two data samples
for (i in user_eng) {
  x <- df_beta_ue[,i]
  y <- df_release_ue[,i]
  
  rg <- range(x, y, na.rm=T)
  
  test <- ks.test(x, y)$statistic
  pvalue <- ks.test(x, y)$p.value
  
  test <- paste("KS Test = ", round(test, 3))
  pvalue <- paste("P-value = ", round(pvalue, 3))
  
  qqplot(x, y, main=i, xlim=rg, ylim=rg, xlab = "Beta", ylab = "Release", pch = 1)
  # mtext(test, side=3)
  text(min(x), max(x), paste(pvalue, "\n", test), adj=c(0,1))
  abline(0,1, col="red")  
}

for (i in user_eng) {
  x <- df_beta_ue[,i]
  y <- df_release_ue[,i]
  
  print(i)
  # print(ad.test(x))
  # print(ad.test(y))
  print(ks.test(x, y))
}

## [1] "num_active_days"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.070619, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "active_hours"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.04493, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "active_hours_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.044246, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "uri_count"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.047413, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "uri_count_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.053957, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "session_length"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.098562, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "session_length_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.073339, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "search_count"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.014407, p-value = 4.652e-09
## alternative hypothesis: two-sided
## 
## [1] "search_count_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.019136, p-value = 1.221e-15
## alternative hypothesis: two-sided
## 
## [1] "num_bookmarks"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.026078, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_pages"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.05463, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_pages_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.053836, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_addons"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.60116, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_unique_domains"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.029154, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_unique_domains_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.03293, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_max_tabs"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.09362, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_max_tabs_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.07981, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_tabs_opened"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.034583, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_tabs_opened_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.032014, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_num_sessions_started"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.11891, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_num_sessions_started_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.11591, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "startup_ms"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.12852, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "install_year"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.018028, p-value = 6.062e-14
## alternative hypothesis: two-sided
## 
## [1] "profile_age"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.041815, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "timezone_offset"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.20833, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "memory_mb"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.074939, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "cpu_cores"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.064122, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "cpu_speed_mhz"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.0464, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "cpu_l2_cache_kb"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.025401, p-value < 2.2e-16
## alternative hypothesis: two-sided

Validation

The QQ plot can be used to compare two continuous distributions.

par(mfrow = c(2, 2))  ## Set up a 2 x 2 plotting space

## QQ plot in R to compare two data samples
for (i in user_eng) {
  x <- df_beta_v_ue[,i]
  y <- df_release_v_ue[,i]
  
  rg <- range(x, y, na.rm=T)
  
  test <- ks.test(x, y)$statistic
  pvalue <- ks.test(x, y)$p.value
  
  test <- paste("KS Test = ", round(test, 3))
  pvalue <- paste("P-value = ", round(pvalue, 3))
  
  qqplot(x, y, main=i, xlim=rg, ylim=rg, xlab = "Beta", ylab = "Release", pch = 1)
  # mtext(test, side=3)
  text(min(x), max(x), paste(pvalue, "\n", test), adj=c(0,1))
  abline(0,1, col="red")  
}

for (i in user_eng) {
  x <- df_beta_v_ue[,i]
  y <- df_release_v_ue[,i]
  
  print(i)
  # print(ad.test(x))
  # print(ad.test(y))
  print(ks.test(x, y))
}

## [1] "num_active_days"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.16585, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "active_hours"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.057657, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "active_hours_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.076585, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "uri_count"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.07132, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "uri_count_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.094754, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "session_length"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.075533, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "session_length_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.039646, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "search_count"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.045374, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "search_count_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.058507, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_bookmarks"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.042296, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_pages"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.081639, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_pages_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.082435, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "num_addons"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.29246, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_unique_domains"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.039839, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_unique_domains_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.054168, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_max_tabs"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.074689, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_max_tabs_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.050656, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_tabs_opened"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.036161, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_tabs_opened_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.052805, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_num_sessions_started"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.097817, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "daily_num_sessions_started_max"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.11694, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "startup_ms"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.1303, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "install_year"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.016919, p-value = 3.642e-14
## alternative hypothesis: two-sided
## 
## [1] "profile_age"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.035079, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "timezone_offset"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.23513, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "memory_mb"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.10938, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "cpu_cores"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.087202, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "cpu_speed_mhz"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.061914, p-value < 2.2e-16
## alternative hypothesis: two-sided
## 
## [1] "cpu_l2_cache_kb"
## 
##  Two-sample Kolmogorov-Smirnov test
## 
## data:  x and y
## D = 0.034682, p-value < 2.2e-16
## alternative hypothesis: two-sided

Observations

• Analyzing only the plots, in general, the distributions are very similar to each other
• Mainly the metrics related to active hours and number of active days, search count, number of pages, daily unique domains and daily number of sessions started
• Comparing only the training and validation plots, we can notice that the variables that presented a more different behavior were: num_active_days, uri_count_max and num_addons
• When I performed the KS (kolmogorov-Smirnov) test, the null hypothesis that both samples come from the same distribution was rejected for all the comparisons. Am I doing something wrong?

User Engagement Discrete Metrics

This section will focus only on user engagement discrete metrics. So, we are going to analyze the following metrics:

• default_search_engine
• is_default_browser
• profile_age_cat
• distro_id_norm
• memory_cat
• cpu_speed_cat
• cpu_cores_cat
• cpu_l2_cache_kb_cat
• cpu_vendor
• os_version
• is_wow64
• fxa_configured
• sync_configured
• locale
• country
• timezone_cat
• label
• normalized_channel
• is_release

Comparing Two Discrete Distributions

Training

par(mfrow = c(2, 2))  ## Set up a 2 x 2 plotting space

## QQ plot in R to compare two data samples
for (i in user_eng_dis) {
  x <- df_beta_ue_dis[,i]
  y <- df_release_ue_dis[,i]
  
  rel_beta <- table(x)/nrow(df_beta_ue_dis) #divide the frequency counts by the total
  beta_bar <- barplot(rel_beta,
        main = "Beta", #Give your chart a title
        ylim=c(0,1), border=F, col = "navy",
        xlab = i, #Label the x axis
        ylab = "Relative Frequency" #Label the y axis
  ) 
  # Add the text 
  text(beta_bar, rel_beta+0.025, paste(round(rel_beta*100), "%", sep="") ,cex=1) 
  
  rel_release <- table(y)/nrow(df_release_ue_dis) #divide the frequency counts by the total
  release_bar <- barplot(rel_release,
        main = "Release", #Give your chart a title
        ylim=c(0,1), border=F, col = "navy",
        xlab = i, #Label the x axis
        ylab = "Relative Frequency" #Label the y axis
  )
  
  # Add the text 
  text(release_bar, rel_release+0.025, paste(round(rel_release*100), "%", sep="") ,cex=1) 
}

Validation

par(mfrow = c(2, 2))  ## Set up a 2 x 2 plotting space

## QQ plot in R to compare two data samples
for (i in user_eng_dis) {
  x <- df_beta_v_ue_dis[,i]
  y <- df_release_v_ue_dis[,i]
  
  rel_beta <- table(x)/nrow(df_beta_v_ue_dis) #divide the frequency counts by the total
  beta_bar <- barplot(rel_beta,
        main = "Beta", #Give your chart a title
        ylim=c(0,1), border=F, col = "navy",
        xlab = i, #Label the x axis
        ylab = "Relative Frequency" #Label the y axis
  ) 
  # Add the text 
  text(beta_bar, rel_beta+0.025, paste(round(rel_beta*100), "%", sep="") ,cex=1) 
  
  rel_release <- table(y)/nrow(df_release_v_ue_dis) #divide the frequency counts by the total
  release_bar <- barplot(rel_release,
        main = "Release", #Give your chart a title
        ylim=c(0,1), border=F, col = "navy",
        xlab = i, #Label the x axis
        ylab = "Relative Frequency" #Label the y axis
  )
  
  # Add the text 
  text(release_bar, rel_release+0.025, paste(round(rel_release*100), "%", sep="") ,cex=1) 
}

Observations

• Analyzing only the plots, in general, the distributions are very similar to each other